The exchange bias (EB) effect, which is the shift of the hysteresis loop of a ferromagnet in direct contact with an antiferromagnet, is highly advantageous for the development of spintronics applications. Carbon (C) has been considered as a potential material in next generation electronics production as well as spintronics devices beyond silicon. Here we show experimental evidence for an EB in C/Co composites. The significant EB needs thermal annealing to occur. X-ray absorption spectra and transmission electron microscopy data of these samples reveal that Co carbides in as grown samples decompose and form graphitic C/Co interfaces after annealing. Using x-ray magnetic circular dichroism we have detected the C spins that are responsible for the EB. These results inspire a theoretical model to investigate the magnetic interactions in graphitic C/Co interfaces and interpret the observed results.